An algebraic expression involving $\sin^6\theta + \cos^6\theta$ and $\sin^4\theta + \cos^4\theta$.

Since the identity holds for all $\theta$, substitute $\theta = 0°$. The numerator becomes $\sin^6(0) + \cos^6(0) - 1 = 0 + 1 - 1 = 0$, and the denominator becomes $\sin^4(0) + \cos^4(0) - 1 = 0 + 1 - 1 = 0$. Using L'Hopital's rule or recognizing the pattern reveals the result is $\frac{3}{2}$.

Students often assume the expression simplifies to 0 just because the individual terms look like they cancel out at specific angles, but applying algebraic identities is necessary for a rigorous proof.

This concept of power reduction is similar to finding higher-order derivatives in calculus; mastering these identities significantly speeds up limit evaluations.